A glass is often used in a display part and a case body in electronic devices such as a mobile phone and a smart phone, and to enhance strength of the glass, a so-called chemically strengthened glass having strength enhanced by forming a surface layer on a glass surface by ion exchange is used. The surface layer is a layer present on a glass surface side and having a refractive index distribution generated by ion exchange, contains at least a compressive stress layer having compressive stress generated therein, and may contain a tensile stress layer present in adjacent to the compressive stress layer at a glass inside side and having tensile stress generated therein. Strength of the chemically strengthened glass is determined by a stress value of a surface layer formed, a depth of a surface compressive stress layer, and the like.
In recent years, a chemically strengthened glass has small glass thickness for reducing its weight. Bending strength of a glass decreases with the decrease of sheet thickness. Therefore, it is necessary to further increase a surface stress value (CS value) in order to enhance bending strength. However, a tensile stress value (CT value) inside a glass increases with the progress of the decrease of sheet thickness and increase of CS, and there are possibilities that a glass finely scatters when collided with sufficient penetration force and fracture occurs from the inside of a glass when CT value further increases. To avoid danger of the fracture, the CT value is generally suppressed to equal to or lower than a CT value at which a glass, when broken, begins to finely scatter.
Patent Document 1 proposes a method of controlling strength of a strengthened glass by defining tensile stress CT inside a glass and adjusting CT value to a certain numerical range. In this method, tensile stress CT (unit: MPa) is calculated by the following formula (1). In the formula, CS is a surface stress value (MPa), DOL is a depth of a compressive stress layer (unit: μm), and t is a sheet thickness (unit: μm). The formula (1) is a limit value investigated in a chemically strengthened glass having a so-called complementary error function profile such that approximation to a linear function of a compressive stress profile inside a glass (hereinafter referred to as triangular approximation) can be relatively acceptable.
                    [                  Math          .                                          ⁢          1                ]                                                                      CT          1                =                              CS            ×            DOL                                (                          t              -                              2                ×                DOL                                      )                                              (        1        )            
In Patent Document 1, CT value is obtained from the formula (1), and a thickness function called nonlinear critical central tension CTlimit is defined as “CTlimit=−38.7×ln(t/1000)+48.2” (formula (2)), is proposed as the upper limit of the CT value defined by the formula (1) and is used as a critical value of the beginning of unacceptable vulnerability.
Patent Document 2 proposes, in an ion-exchanged glass based on non-error functional compressive stress profile, a method of controlling strength of a strengthened glass by defining tensile stress CT inside the glass by a method different from the formula (1) and setting CT value to a certain numerical range. In this method, the total tensile stress CT (unit: MPa) is calculated by “CT=(CS1×DOL1)/(t−2×DOL1)+(CS2×DOL2)/(t−2×DOL2)” (formula (3)). Here, CS1 is a surface stress value (MPa) that is the maximum of compressive stress positioned under the surface of a glass, CS2 is a surface stress value (MPa), DOL1 is a depth (unit: μm) of a compressive stress layer, DOL2 is a depth (unit: μm) corresponding to CS1, and t is a sheet thickness (unit: μm). In the light of the above, a thickness function called brittleness limit CTlimit is defined as “CTlimit=−36.7×ln(t/1000)+48.7” (formula (4)) similar to CTlimit in Patent Document 1, and is proposed as the upper limit of the CT value calculated by the formula (2).